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NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers

NCERT for class 7 maths chapter 13 exponents and powers topic 13.2 exponents

Question:(i) Express:

729 as a power of 3

Answer:

729 as a power of 3 is given as

729=3\times 3\times 3\times 3\times 3\times 3=3^6

Question:(ii) Express:

128 as a power of 2

Answer:

128 as a power of 2 can be given as

128=2\times 2\times2 \times 2\times 2\times 2\times 2=2^7

Question:(iii) Express:

343 as a power of 7

Answer:

343 as a power of 7 can be givena as

343=7\times 7\times 7=7^3

NCERT solutions for class 7 maths chapter 13 exponents and powers exercise 13.1

Question: 1(i) Find the value of:

(i)2^{6}

Answer:

the value of 2^6 is given by

2\times 2\times2 \times 2\times2 \times 2=64

Question: 1(ii) Find the value of:

(ii)9^{3}

Answer:

the value of (ii)9^{3} is given by

9\times 9\times 9=729

Question:1(iii) Find the value of:

(iii)11^{2}

Answer:

the value of (iii)11^{2} is given by

11\times 11=121

Question: 1(iv) Find the value of:

(iv)5^{4}

Answer:

the value of (iv)5^{4} is given by

5^4=5\times 5\times 5\times 5=625

Question: 2 Express the following in exponential form:

(i)6\times 6\times 6\times 6(ii)t\times t(iii)b\times b\times b\times b(iv)5\times 5\times 7\times 7\times 7

(v)2\times 2\times a\times a(vi)a\times a\times a\times c\times c\times c\times c\times d

Answer:

(i)6\times 6\times 6\times 6 can be given as

6^4 .

(ii)t\times t can be given as t^2 .

(iii)b\times b\times b\times b can be given as b^4 .

(iv)5\times 5\times 7\times 7\times 7 can be given as

5^2\times 7^3 .

(v)2\times 2\times a\times a can be given as

2^2\times a^2 .

(vi)a\times a\times a\times c\times c\times c\times c\times d can be given as

a^3\times c^4\times d .

Question: 3 Express each of the following numbers using exponential notation:

(i) 512 (ii) 343 (iii) 729 (iv) 3125

Answer:

(i) 512

2

512

2

256

2

128

2

64

2

32

2

16

2

8

2

4

2

2

1

512=2\times 2\times2 \times2 \times 2\times 2\times2 \times 2\times 2=2^9

(ii) 343

7

343

7

49

7

7

1

343=7\times 7\times 7=7^3

(iii)729

3

729

3

243

3

81

3

27

3

9

3

3

1

729=3\times 3\times 3\times 3\times 3\times 3=3^6

(iv)3125

5

3125

5

625

5

125

5

25

5

5

1

3125=5\times 5\times 5\times 5\times 5=5^5

Question: 4 Identify the greater number, wherever possible, in each of the following?

(i)4^{3}or \: 3^{4}(ii) 5^{3}or \: 3^{5}(iii) 2^{8}or \: 8^{2}(iv) 100^{2}or \: 2^{100}(v) 2^{10}or \: 10^{2}

Answer:

(i)4^{3}or \: 3^{4}

4^3=4\times 4\times 4=64

3^4=3\times 3\times 3\times 3=81

since 81> 64

3^4 is greater than 4^3

(ii) 5^{3}or \: 3^{5}

5^3=5\times 5\times 5=125

3^5=3\times 3\times 3\times 3\times 3=243

since 243> 125

3^5 is greater than 5^3

(iii) 2^{8}or \: 8^{2}

2^8=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=256

8^2=8\times 8=64

since 256 > 64

2^8 is greater than 8^2

(iv) 100^{2}or \: 2^{100}

100^2=100\times 100=10000

2^1^0^0=2\times 2\times 2\times 2\times 2...........till\, 100\, times\, 2

since 2^1^0^0> 100^2

2^1^0^0 is greater than 100^2

(v) 2^{10}or \: 10^{2}

2^1^0=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=1024

10^2=10\times 10=100

since 1024> 100

<img alt="2^1^0" height="16"

src="https://lh4.googleusercontent.com/I3HS3zuzL_njxaOw4nMet5jP4HXF5cz7f1G74MyN7vkadpB-kWjNUeMbbBQdaFyt9kMcfFEPbhioXB0Yg07ol3Qe8UVf_l8jM5_e7JbuokRxaLHBBeCXJADBNdq8lUwYAgmJPPM" style="margin-left: 0px; margin-top: 0px;" width="21" /> is greater than 10^2

Question: 5 Express each of the following as product of powers of their prime factors:

(i) 648 (ii) 405 (iii) 540 (iv) 3,600

Answer:

(i) 648

2

648

2

324

2

162

2

81

3

27

3

9

3

3

1

648=2^3\times 3^4

(ii) 405

5

405

3

81

3

27

3

9

3

3

1

405=5\times 3^4

(iii)540

2

540

2

270

3

135

3

45

3

15

5

5

1

540=2^2\times 3^3\times 5

(iv) 3600

2

3600

2

1800

2

900

2

450

3

225

3

75

5

25

5

5

1

3600=2^4\times 3^2\times 5 ^2

Question: 6(i) Simplify:

(i)2\times 10^{3}

Answer:

(i)2\times 10^{3}

can be simplified as

2\times 10\times 10\times 10=2000

Question: 6(ii) Simplify:

(ii)7^{2}\times 2^{2}

Answer:

(ii)7^{2}\times 2^{2}

can be simplified as

7\times 7\times 2\times 2=196

Question: 6(iii) Simplify:

(iii) 2^{3}\times 5

Answer:

(iii) 2^{3}\times 5

can be simplified as

2\times 2\times 2\times 5=40

Question: 6(iv) Simplify:

(iv) 3\times 4^{4}

Answer:

(iv) 3\times 4^{4}

can be simplified as

3 \times 4\times 4\times 4\times 4=768

Question: 6(v) Simplify:

(v)0\times 10^{2}

Answer:

(v)0\times 10^{2}

can be simplified as

0\times 10\times 10=0

Question: 6(vi) Simplify:

(vi)5^{2}\times 3^{3}

Answer:

(vi)5^{2}\times 3^{3}

can be simplified as

5\times 5\times 3\times3 \times 3=675

Question: 6(vii) Simplify:

(vii) 2^{4}\times 3^{2}

Answer:

(vii) 2^{4}\times 3^{2}

can be simplified as

2\times 2\times 2\times 2\times 3\times 3=144

Question: 6(v iii) Simplify:

(viii)3^{2}\times 10^{4}

Answer:

(viii)3^{2}\times 10^{4}

can be simplified as

3\times3 \times 10\times 10\times10 \times 10=90000

Question: 7(i) Simplify:

(i)(-4)^{3}

Answer:

(i)(-4)^{3}

can be simplified as

-4\times -4\times -4=-64

Question: 7(ii) Simplify:

(ii) (-3)\times (-2)^{3}

Answer:

(ii) (-3)\times (-2)^{3}

can be simplified as

-3\times -2\times -2\times -2=24

Question: 7(iii) Simplify:

(iii) (-3)^{2}\times (-5)^{2}

Answer:

(iii) (-3)^{2}\times (-5)^{2}

can be simplified as

(-3)\times (-3)\times (-5)\times (-5)=225

Question: 7(iv) Simplify:

(iv) (-2)^{3}\times (-10)^{3}

Answer:

(iv) (-2)^{3}\times (-10)^{3}

can be simplified as

(-2)\times (-2)\times (-2)\times- 10\times -10\times -10=8000

Question: 8 Compare the following numbers:

(i) 2.7\times 10^{12} ;1.5\times 10^{8}(ii) 4\times 10^{14} ;3\times 10^{17}

Answer:

(i) 2.7\times 10^{12} ;1.5\times 10^{8}

on comparing exponents of base 10.

2.7\times 10^{12} > 1.5\times 10^{8}

(ii) 4\times 10^{14} ;3\times 10^{17}

on comparing exponents of base 10.

4\times 10^{14} < 3\times 10^{17}

NCERT solutions for class 7 maths chapter 13 exponents and powers topic 13.3.1

Question:(i) Simplify and write in exponential form:

(i)2^{5}\times 2^{3}

Answer:

(i)2^{5}\times 2^{3}

can be simplified as

2^{5+3}=2^8

Question:(ii) Simplify and write in exponential form:

(ii) p^{3}\times p^{2}

Answer:

(ii) p^{3}\times p^{2}

can be simplified as

p(3+2)=p^5

Question:(iii) Simplify and write in exponential form:

(iii)\: 4^{3}\times 4^{2}

Answer:

(iii)\: 4^{3}\times 4^{2}

can be simplified as

4^{(3+2)}=4^5

Question:(iv) Simplify and write in exponential form:

(iv)\: a^{3}\times a^{2}\times a^{7}

Answer:

(iv)\: a^{3}\times a^{2}\times a^{7}

can be simplified as

a^{(3+2+7)}=a^1^2

Question:(v) Simplify and write in exponential form:

(v)\: 5^{3}\times 5^{7}\times 5^{12}

Answer:

(v)\: 5^{3}\times 5^{7}\times 5^{12}

can be simplified as

5^{(3+7+12)}=5^2^2

Question:(vi) Simplify and write in exponential form:

(vi)\: (-4)^{100}\times (-4)^{20}

Answer:

(vi)\: (-4)^{100}\times (-4)^{20}

can be simplified as

(-4)^{(100+20)}=(-4)^{120}

NCERT solutions for class 7 maths chapter 13 exponents and powers topic 13.3.2

Question: 1 Simplify and write in exponential form: (eg., 11^{6}\div 11^{2}= 11^{4} )

(i)\: 2^{9}\div 2^{3}(ii)\: 10^{8}\div 10^{4}(iii)\: 9^{11}\div 9^{7}(iv)\: 20^{15}\div 20^{13}(v)\: 7^{13}\div 7^{10}

Answer:

(i)\: 2^{9}\div 2^{3}

can be simplified as 2^{9-3}=2^6

(ii)\: 10^{8}\div 10^{4}

can be simplified as 10^{(8-4)}=10^4

(iii)\: 9^{11}\div 9^{7}

can be simplified as 9^{(11-7)}=9^4

(iv)\: 20^{15}\div 20^{13}

can be simplified as 20^{(15-13)}=20^2

(v)\: 7^{13}\div 7^{10}

can be simplified as 7^{(13-10)}=7^3

NCERT solutions forclass 7 maths chapter 13 exponents and powers topic 13.3.3

Question: Simplify and write the answer in exponential form:

(i)\: (6^{2})^{4}(ii)\: (2^{2})^{100}(iii)\: (7^{50})^{2}(iv)\: (5^{3})^{7}

Answer:

(i)\: (6^{2})^{4}

can be simplified as 6^{(2\times 4)}=6^8

(ii)\: (2^{2})^{100}

can be simplified as 2^{(2\times 100)}=2^{200}

(iii)\: (7^{50})^{2}

can be simplified as 7^{(50\times 2)}=7^{100}

(iv)\: (5^{3})^{7}

can be simplified as 5^{(3\times 7)}=5^{21}

NCERT solutions for class 7 maths chapter 13 exponents and powers topic 13.3.4

Question: Put into another form using a^{m}\times b^{m}= (ab)^{m} :

(i)\: 4^{3}\times 2^{3}(ii)\: 2^{5}\times b^{5}(iii)\: a^{2}\times t^{2}(iv)\: 5^{6}\times (-2)^{6}(v)\: (-2)^{4}\times (-3)^{4}

Answer:

(i)\: 4^{3}\times 2^{3}

can be simplified as (4\times 2)^3=8^3

(ii)\: 2^{5}\times b^{5}

can be simplified as (2\times b)^5=(2b)^5

(iii)\: a^{2}\times t^{2}

can be simplified as (a\times t)^2=at^2

(iv)\: 5^{6}\times (-2)^{6}

can be simplified as (5\times (-2))^6=-10^6

(v)\: (-2)^{4}\times (-3)^{4}

can be simplified as ((-2)\times (-3))^4= 6^4

NCERT solutions for class 7 maths chapter 13 exponents and powers topic 13.3.5

Question: Put into another form using a^{m}\div b^{m}= (\frac{a}{b})^{m} :

(i)\: 4^{5}\div 3^{5}(ii)\: 2^{5}\div b^{5}(iii)\: (-2)^{3}\div b^{3}(iv)\: p^{4}\div q^{4}(v)\: 5^{6}\div (-2)^{6}

Answer:

<img alt="(i)\: 4^{5}\div 3^{5}" height="20"

src="https://lh6.googleusercontent.com/yahwdkqP5TpTF80JP_-5EuxxOZDfcg_tyVILq3o80toSWOiv1ICmO1kl68txcnIVF-MRD6DyIGDST3itGYZw3JxF_3HZF21iYEyGblIWN2LSOuZlHq_rrZiLS40nwJxrIkA9sN8" style="margin-left: 0px; margin-top: 0px;" width="77" />

can be simplified as

\left ( \frac{4}{3} \right )^{5}

(ii)\: 2^{5}\div b^{5}

can be simplified as

\left ( \frac{2}{b} \right )^{5}

(iii)\: (-2)^{3}\div b^{3}

can be simplified as

\left ( \frac{-2}{b} \right )^{3}

(iv)\: p^{4}\div q^{4}

can be simplified as

\left ( \frac{p}{q} \right )^{4}

(v)\: 5^{6}\div (-2)^{6}

can be simplified as

\left ( \frac{5}{-2} \right )^{6}

NCERT solutions for class 7 maths chapter 13 exponents and powers exercise 13.2

Question: 1 Using laws of exponents, simplify and write the answer in exponential form:

(i)\: 3^{2}\times 3^{4}\times 3^{8}(ii)\: 6^{15}\div 6^{10}(iii)\: a^{3}\times a^{2}(iv)\: 7^{x}\times 7^{2}

(v)\:(5^{2})^{3}\div 5^{3}(vi)\:2^{5}\times 5^{5}(vii)\:a^{4}\times b^{4}(viii)\:(3^{4})^{3}

(ix)\:(2^{20}\div 2^{15})\times 2^{3}(x)\:8^{t}\div 8^{2}

Answer:

(i)\: 3^{2}\times 3^{4}\times 3^{8}

can be simplified as 3^{(2+4+8)}=3^{14}

(ii)\: 6^{15}\div 6^{10}

can be simplified as 6^{(15-10)}=6^{5}

(iii)\: a^{3}\times a^{2}

can be simplified as a^{(3+2)}=a^{5}

(iv)\: 7^{x}\times 7^{2}

can be simplified as 7^{(x+2)}=7^{(x+2)}

(v)\:(5^{2})^{3}\div 5^{3}

can be simplified as 5^{(2\times 3)}\div 5^{(3)}=5^6\div 5^3=5^{6-3}=5^3

(vi)\:2^{5}\times 5^{5}

can be simplified as

(2\times5)^{5}=10^5

(vii)\:a^{4}\times b^{4}

can be simplified as (ab)^4

(viii)\:(3^{4})^{3}

can be simplified as 3^{4\times 3}=3^{12}

(ix)\:(2^{20}\div 2^{15})\times 2^{3}

can be simplified as 2^{(20-15)}\times 2^3=2^5\times 2^3=2^{(5+3)}=2^8

(x)\:8^{t}\div 8^{2}

can be simplified as 8^{(t-2)}

Question:2(i) Simplify and express each of the following in exponential form:

(i)\: \frac{2^{3}\times 3^{4}\times 4}{3\times 32}

Answer:

(i)\: \frac{2^{3}\times 3^{4}\times 4}{3\times 32}

can be simplified as

=\frac{2^3\times 3^4\times 2^2}{3\times 2^5}

=\frac{ 2^{(3+2)} \times 3^4}{3\times 2^5}

=\frac{ 2^{5} \times 3^4}{3\times 2^5}

= 2^{(5-5)} \times 3^{(4-1)}

=3^3

Question: 2(ii) Simplify and express each of the following in exponential form:

(ii)\: ((5^{2})^{3}\times 5^{4})\div 5^{7}

Answer:

(ii)\: ((5^{2})^{3}\times 5^{4})\div 5^{7}

can be simplified as

=[5^{(2\times 3)}\times 5^4]\div 5^7

=[5^{6}\times 5^4]\div 5^7

=[5^{(6+4)}]\div 5^7

=[5^{10}]\div 5^7

=5^{10-7}

=5^3

Question: 2(iii) Simplify and express each of the following in exponential form:

(iii)\: 25^{4}\div 5^{3}

Answer:

(iii)\: 25^{4}\div 5^{3}

can be simplified as

=(5^2)^4\div 5^3

=5^{(2\times 4)}\div 5^3

=5^8\div 5^3

=5^{(8-3)}

=5^{5}

Question: 2(iv) Simplify and express each of the following in exponential form:

(iv)\: \frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}}

Answer:

(iv)\: \frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}}

can be simplified as

= \frac{3\times 7^{2}\times 11^{8}}{3\times 7\times 11^{3}}

=3^{(1-1)}\times 7^{(2-1)}\times 11^{(8-3)}

=3^{0}\times 7^{1}\times 11^{5}

=7^{1}\times 11^{5}

Question: 2(v) Simplify and express each of the following in exponential form:

(v)\: \frac{3^{7}}{3^{4}\times 3^{3}}

Answer:

(v)\: \frac{3^{7}}{3^{4}\times 3^{3}}

can be simplified as

=\frac{3^7}{3^{4+3}}

=\frac{3^7}{3^{7}}

=3^{(7-7)}

=3^0

=1

Question: 2(vi) Simplify and express each of the following in exponential form:

(vi)\: 2^{0}+3^{0}+4^{0}

Answer:

(vi)\: 2^{0}+3^{0}+4^{0}

can be simplified as

=1+1+1

=3

Question: 2(vii) Simplify and express each of the following in exponential form:

(vii)\: 2^{0}\times 3^{0}\times 4^{0}

Answer:

(vii)\: 2^{0}\times 3^{0}\times 4^{0}

can be simplified as

=1\times 1\times 1=1

Question: 2(viii) Simplify and express each of the following in exponential form:

(viii)\: (3^{0}+2^{0})\times 5^0

Answer:

(viii)\: (3^{0}+2^{0})\times 5^0

can be simplified as

=(1+1)\times 1

=2\times 1

=2

Question: 2(ix) Simplify and express each of the following in exponential form:

(ix)\: \frac{2^{8}\times a^{5}}{4^{3}\times a^{3}}

Answer:

(ix)\: \frac{2^{8}\times a^{5}}{4^{3}\times a^{3}}

can be simplified as

=\frac{2^{8}\times a^{5}}{(2^2)^{3}\times a^{3}}

=\frac{2^{8}\times a^{5}}{2^{6}\times a^{3}}

=2^{(8-6)}\times a^{(5-3)}

=2^{(2)}\times a^{(2)}

=(2a)^2

Question: 2(x) Simplify and express each of the following in exponential form:

(x)\: (\frac{a^{5}}{a^{3}})\times a^{8}

Answer:

(x)\: (\frac{a^{5}}{a^{3}})\times a^{8}

can be simplified as

=a^{(5-3)}\times a^8

=a^{(2)}\times a^8

=a^{(2+8)}

=a^{(10)}

Question: 2(xi) Simplify and express each of the following in exponential form:

(xi)\: \frac{4^{5}\times a^{8}b^{3}}{4^{5}\times a^{5}b^{2}}

Answer:

(xi)\: \frac{4^{5}\times a^{8}b^{3}}{4^{5}\times a^{5}b^{2}}

can be simplified as

=4^{(5-5)}\times a^{(8-5)}\times b^{(3-2)}

=4^{0}\times a^{3}\times b^{1}

= a^{3}\times b

Question:2(xii) Simplify and express each of the following in exponential form:

<img alt="(xii)\: (2^{3}\times 2)^{2}" height="20"

src="https://lh3.googleusercontent.com/HKUs4jh8ng1_gjPCZHSe6T4Hs3F8aYa2XlfP37cmqFJn3KEIzcQimFrs49AmOHZBCcABvYkBylsRsZHPMxw6M7vvxzVdpdIqB0m1rhlLukcKr5CXU-YPcxUFBIEQGZ44qZVPUm8" style="margin-left: 0px; margin-top: 0px;" width="107" />

Answer:

(xii)\: (2^{3}\times 2)^{2}

can be simplified as

=2^{(3+1)}^2

=(2^{(4)})^2

=2^{(4 \times 2)}

=2^8

Question: 3 Say true or false and justify your answer:

(i)\: 10\times 10^{11}=100^{11}(ii)\: 2^{3}> 5^{2}(iii)\: 2^{3}\times 3^{2}= 6^{5}(iv)\: 3^{0}=(1000)^{0}

Answer:

(i)\: 10\times 10^{11}=100^{11}

can be simplified as

LHS:10^{(1+11)}

=10^{(12)}

Since , LHS \neq RHS

Thus, it is false

(ii)\: 2^{3}> 5^{2}

can be simplified as

LHS=2^3=8

RHS=5^2=25

Since, LHS\ngtr RHS

Thus, it is false

(iii)\: 2^{3}\times 3^{2}= 6^{5}

can be simplified as

LHS:2^3\times 3^2=8\times 9=72

RHS: 6^5=7776

Since , LHS \neq RHS

Thus, it is false

(iv)\: 3^{0}=(1000)^{0}

can be simplified as

LHS: 3^0=1

RHS:1000^0=1

Since, LHS = RHS

Thus, it is true.

Question: 4 Express each of the following as a product of prime factors only in exponential form:

(i)\: 108\times 192(ii)\: 270(iii)\: 729\times 64(iv)\: 768

Answer:

(i)\: 108\times 192

2

108

2

54

3

27

3

9

3

3

1

2

192

2

96

2

48

2

24

2

12

2

6

3

3

1

108\times 192=(2^2\times 3^3)\times (2^6\times 3)

=2^{(2+6)}\times 3^{(3+1)}

=2^8\times 3^4

(ii)\: 270

2

270

3

135

3

45

3

15

5

5

1

270=2\times 3^3\times 5

(iii)\: 729\times 64

3

729

3

243

3

81

3

27

3

9

3

3

1

2

64

2

32

2

16

2

8

2

4

2

2

1

729\times 64=3^6\times 2^6

(iv)\: 768

2

768

2

384

2

192

2

96

2

48

2

24

2

12

2

6

3

3

1

768=2^8\times 3

Question: 5(i) Simplify:

(i)\: \frac{(2^{5})^{2}\times 7^{3}}{8^{3}\times 7}

Answer:

(i)\: \frac{(2^{5})^{2}\times 7^{3}}{8^{3}\times 7}

can be simplified as

= \frac{2^{(5\times 2)}\times 7^{3}}{(2^3)^{3}\times 7}

= \frac{2^{10}\times 7^{3}}{(2^{(3\times 3)})\times 7}

= \frac{2^{10}\times 7^{3}}{(2^{9})\times 7}

=2^{(10-9)}\times 7^{(3-1)}

=2\times 7^{2}

=2\times49=98

Question: 5(ii) Simplify:

(ii)\frac{25\times 5^{2}\times t^{8}}{10^{3}\times t^{4}}

Answer:

(ii)\frac{25\times 5^{2}\times t^{8}}{10^{3}\times t^{4}}

can be simplified as

=\frac{5^2\times 5^{2}\times t^{8}}{(2\times 5)^{3}\times t^{4}}

=\frac{5^{(2+2)}\times t^{8}}{2^3\times 5^{3}\times t^{4}}

=\frac{5^{4}\times t^{8}}{2^3\times 5^{3}\times t^{4}}

=\frac{5^{4-3}\times t^{(8-4)}}{2^3}

=\frac{5\times t^{4}}{2^3}

=\frac{5 t^{4}}{8}

Question: 5(iii) Simplify:

(iii)\: \frac{3^{5}\times 10^{5}\times 25}{5^{7}\times 6^{5}}

Answer:

(iii)\: \frac{3^{5}\times 10^{5}\times 25}{5^{7}\times 6^{5}}

can be simplified as

= \frac{3^{5}\times (2\times 5)^{5}\times 5^2}{5^{7}\times (2\times 3)^{5}}

= \frac{3^{5}\times 2^5 \times 5^{5}\times 5^2}{5^{7}\times 2^5 \times 3^{5}}

= 3^{(5-5)} \times 2^{(5-5)} \times 5^{(5+2-7)}

= 3^{0} \times 2^{0} \times 5^{0}

= 1 \times 1 \times 1=1

NCERT solutions for class 7 maths chapter 13 exponents and powers topic 13.6

Question: Expand by expressing powers of 10 in the exponential form:

(i) 172 (ii) 5,643 (iii) 56,439 (iv) 1,76,428

Answer:

(i) 172

172=100+70+2

=100+(7\times 10)+2

=1\times 10^2+(7\times 10^1)+2\times 10^0

(ii) 5,643

5643=5000+600+40+3

=5\times 1000+6\times 100+4\times 10+3

=5\times 10^3+6\times 10^2+4\times 10^1+3\times 10^0

(iii) 56,439

56439=50000+6000+400+30+9

=5\times 10000+6\times 1000+4\times 100+3\times 10+9

=5\times 10^4+6\times 10^3+4\times 10^2+3\times 10^1+9\times 10^0

(iv) 1,76,428

176428=100000+70000+6000+400+20+8

=1\times 100000+7\times 10000+6\times 1000+4\times 100+2\times 10+8

=1\times 10^5+7\times 10^4+6\times 10^3+4\times 10^2+2\times 10^1+8\times 10^0

NCERT solutions for class 7 maths chapter 13 exponents and powers exercise 13.3

Question: 1 Write the following numbers in the expanded forms:

279404, 3006194, 2806196, 120719, 20068

Answer:

(i) 279404

279404=200000+70000+9000+400+00+4

=2\times 100000+7\times 10000+9\times 1000+4\times 100+0\times 10+4\times 1

=2\times 10^5+7\times 10^4+9\times 10^3+4\times 10^2+0\times 10^1+4\times 10^0

(ii) 3006194

3006194=3000000+0+0+6000+100+90+4

=3\times 10^6+0\times 10^5+0\times 10^4+6\times 10^3+1\times 10^2+9\times 10^1+4\times 10^0

(iii) 2806196

2806196=2000000+800000+0+6000+100+90+6

=2\times 1000000+8\times 100000+0\times 10000+6\times 1000+1\times 100+9\times 10+6\times 1

=2\times 10^6+8\times 10^5+0\times 10^4+6\times 10^3+1\times 10^2+9\times 10^1+6\times 10^0

(IV) 120719

120719=100000+20000+0+700+10+9

=1\times 100000+2\times 10000+0\times 1000+7\times 100+1\times 10+9\times 1=1\times 10^5+2\times 10^4+0\times 10^3+7\times 10^2+1\times 10^1+9\times 10^0

(V) 20068

20068=20000+0+0+60+8

=2\times 10000+0\times 1000+0\times 100+6\times 10+8\times 1

=2\times 10^4+0\times 10^3+0\times 10^2+6\times 10^1+8\times 10^0

Question: 2 Find the number from each of the following expanded forms:

(a)\: 8\times 10^{4}+6\times 10^{3}+0\times 10^{2}+4\times 10^{1}+5\times 10^{0}

(b)\: 4\times 10^{5}+5\times 10^{3}+3\times 10^{2}+2\times 10^{0}

(c)\: 3\times 10^{4}+7\times 10^{2}+5\times 10^{0}

(d)\: 9\times 10^{5}+2\times 10^{2}+3\times 10^{1}

Answer:

(a)\: 8\times 10^{4}+6\times 10^{3}+0\times 10^{2}+4\times 10^{1}+5\times 10^{0}

=8\times 10000+6\times 1000+0\times 100+4\times 10+5\times 1

=80000+6000+000+40+5

=86045

(b)\: 4\times 10^{5}+5\times 10^{3}+3\times 10^{2}+2\times 10^{0}

=4\times 100000+0\times 10000+5\times 1000+3\times 100+0\times 10+2\times 1

=400000+00000+5000+300+00+2

<img alt="=405302" height="14"

src="https://lh5.googleusercontent.com/A1vx8zdaeENUp9KLNFmphH3s3x12mEV0ySa0M1tYKPqrA7GYRrB_O0C3BsGdMgudT9TBD1S0YvjsruztcRxREZMo4nFb9Bk81Lwb9cgMl4cQ_xpNWPpIOyFFmfsAkuutOh8DByk" style="margin-left: 0px; margin-top: 0px;" width="73" />

(c)\: 3\times 10^{4}+7\times 10^{2}+5\times 10^{0}

=3\times 10000+0\times 1000+7\times 100+0\times 10+5\times 1

=30000+0000+700+00+5

=30705

(d)\: 9\times 10^{5}+2\times 10^{2}+3\times 10^{1}

=9\times 100000+0\times 10000+0\times 1000+2\times 100+3\times 10+0\times 1

=900000+00000+0000+200+30+0

=900230

Thus, the above problems are simplified in simpler forms.

Question: 3 Express the following numbers in standard form:

(i) 5,00,00,000 (ii) 70,00,000 (iii ) 3,18,65,00,000 (iv) 3,90,878 (v) 39087.8 (vi) 3908.78

Answer:

(i) 5,00,00,000

50000000=5\times 10000000=5\times 10^7

(ii) 70,00,000

7000000=7\times 1000000=7\times 10^6

(iii ) 3,18,65,00,000

3186500000=31865\times 100000

=3.1865\times 10000 \times 100000

=3.1865\times 10^9

(iv) 3,90,878

=3.90878\times 100000

=3.90878\times 10^5

(v) 39087.8

=3.90878\times 10000

=3.90878\times 10^4

(vi) 3908.78

=3.90878\times 1000

=3.90878\times 10^3

Question: 4 Express the number appearing in the following statements in standard form.

(a) The distance between Earth and Moon is 384,000,000 m.

(b) Speed of light in vacuum is 300,000,000 m/s.

(c) Diameter of the Earth is 1,27,56,000 m.

(d) Diameter of the Sun is 1,400,000,000 m.

(e) In a galaxy there are on an average 100,000,000,000 stars.

(f) The universe is estimated to be about 12,000,000,000 years old.

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

(i) The earth has 1,353,000,000 cubic km of sea water.

(j) The population of India was about 1,027,000,000 in March, 2001.

Answer:

(a) The distance between Earth and Moon = 384,000,000 m

=384\times 1000000

=3.84 \times 100\times 1000000

=3.84 \times 10^8m

(b) Speed of light in vacuum =300,000,000 m/s.

=3\times 100000000

=3\times 10^8

(c) Diameter of the Earth = 1,27,56,000 m.

=12756\times 1000

=1.2756\times 10000\times 1000

=1.2756\times 10^7m

(d) Diameter of the Sun = 1,400,000,000 m.

=14\times 100000000

=14\times 10^8m

=1.4\times 10^9m

(e) In a galaxy there are on an average = 100,000,000,000 stars.

=1\times 100000000000

=1\times 10^{11}

(f) The universe is estimated to be about= 12,000,000,000 years old.

=1.2\times 10000000000

=1.2\times 10^{10}years

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated = 300,000,000,000,000,000,000 m.

=3\times 100000000000000000000000000000

=3 \times 10^{19}

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

60,230,000,000,000,000,000,000

= 6023\times 10000,000,000,000,000,000

= 6023\times 10^{19}

(i) The earth has 1,353,000,000 cubic km of seawater.

=1.353\times 1000000000

=1.353\times 10^9 km^3

(j) The population of India was about 1,027,000,000 in March 2001.

=1.027\times 1000000000

=1.027\times 10^9

 

Responsive Table

Chapter No.Chapter Name
Chapter 1 NCERT solutions for class 7 maths chapter 1 Integers
Chapter 2 NCERT solutions for class 7 maths chapter 2 Fractions and Decimals
Chapter 3 NCERT solutions for class 7 maths chapter 3 Data Handling
Chapter 4 NCERT solutions for class 7 maths chapter 4 Simple Equations
Chapter 5 NCERT solutions for class 7 maths chapter 5 Lines and Angles
Chapter 6 NCERT solutions for class 7 maths chapter 6 The Triangle and its Properties
Chapter 7 NCERT solutions for class 7 maths chapter 7 Congruence of Triangles
Chapter 8 NCERT solutions for class 7 maths chapter 8 comparing quantities
Chapter 9 NCERT solutions for class 7 maths chapter 9 Rational Numbers
Chapter 10 NCERT solutions for class 7 maths chapter 10 Practical Geometry
Chapter 11 NCERT solutions for class 7 maths chapter 11 Perimeter and Area
Chapter 12 NCERT solutions for class 7 maths chapter 12 Algebraic Expressions
Chapter 13 NCERT solutions for class 7 maths chapter 13 Exponents and Powers
Chapter 14 NCERT solutions for class 7 maths chapter 14 Symmetry
Chapter 15 NCERT solutions for class 7 maths chapter 15 visualising-solid-shapes
ncert-solutions-class-7-maths-ch-13-exponents-and-powers Anonymous Clear IIT Medical Review 4.9 of 5
NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers NCERT for class 7 maths chapter 13 exponents and powers topic 13.2 expo...

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